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" IF a straight line be drawn parallel to one of the sides of a triangle, it shall cut the other sides, or those produced, proportionally ; and if the sides, or the sides produced, be cut proportionally, the straight line which joins the points of section... "
The figures of Euclid with the enunciations, as printed in Euclid's Elements ... - Page 54
by Euclides - 1840
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Euclid's Elements of geometry, transl. To which are added, algebraic ...

Euclides - 1826 - 226 pages
...parallelograms having equal bases, are to each other as their altitudes. PROPOSITION II. THEOREM. У a right line be drawn parallel to one of the sides of a triangle, it shall cut the sides of the triangle proportionally j and if the sides of a triangle be cut proportionally,...
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Elements of Geometry: With Notes

John Radford Young - Euclid's Elements - 1827 - 228 pages
...; but by hypothesis, A2 : B" :': A : C, hence (Prop. IX. Cor. 3. BV), Q=C. PROPOSITION V. THEOREM. If a straight line be drawn parallel to one of the sides of a triangle, it shall cut the other sides, or those produced, proportionally ; and conversely, if the sides or the...
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The Elements of Euclid: The Errors by which Theon, Or Others, Have Long ...

Robert Simson - Trigonometry - 1827 - 546 pages
...construction be made as in the pro, . - position, the demonstration will be the same. PROP. II. THEOR. 3ee N. If a straight line be drawn parallel to one of the sides of a triangle, it shall cut the other sides, or these produced, proportionally : and if the sides, or the sides produced,...
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Elements of Geometry: With Notes

John Radford Young - Euclid's Elements - 1827 - 246 pages
...triangle are respectively equal to those of another, the triangles are similar. Cor. 2. Therefore if a line be drawn parallel to one of the sides of a triangle it will cut off a triangle similar to the whole. PROPOSITION x. THEOREM. {Converse of Prop. IX.} The angles of...
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Elements of Geometry: Being Chiefly a Selection from Playfair's Geometry

John Playfair - Geometry - 1829 - 210 pages
...BOOK VI. Triangles, and also parallelograms, of the same altitude are to one another as their bases. If a straight line be drawn parallel to one of the sides of a triangle it will cut the other two sides proportionally. If any angle of a triangle be bisected by a straight line which cuts the...
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The Elements of Euclid: Viz, the First Six Books, Together with the Eleventh ...

Euclid, Robert Simson - Geometry - 1829 - 548 pages
...: then, if the same construction be made as in the proposition, the demonstration will be the same. PROP. II. THEOR. IF a straight line be drawn parallel to one of the sides of a triangle, it shall cut the other sides, or those produced, proportionally ; and if the sides, or the sides produced,...
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The Elements of Euclid; viz. the first six books, together with the eleventh ...

Euclides - 1834 - 518 pages
...construction be made aq in the proposition, the demonstration will be the same. PROPOSITION II. ^ See N. THEOR. — If a straight line be drawn parallel to one of the sides of a triangle, it shall cut the other sides, or these produced, proportionally : and if the tides, or the sides produced,...
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The Elements of Euclid: Viz. the First Six Books, Together with the Eleventh ...

Euclid - 1835 - 540 pages
...another. Then, if the same construction be made as in the proposition, the demonstration will be the same. PROP. II. THEOR. If a straight line be drawn parallel to one of the See N. sides of a triangle, it will cut the other sides, or the other sides produced, proportionally...
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The Element of Geometry

John Playfair - Geometry - 1836 - 148 pages
...base and altitude, therefore triangles of equal altitude are to one another as their bases. PROP. III. THEOR. \ If a straight line be drawn parallel to one of the sides of a triangle, it shall cut the other sides, or these produced, proportionally ; and if the sides, or the sides produced...
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The First Six and the Eleventh and Twelfth Books of Euclid's Elements: With ...

Euclid, James Thomson - Geometry - 1837 - 410 pages
...triangle ADE ; and * The enunciation of this proposition, as given by Dr. Simson, is as follows : " If a straight line be drawn parallel to one of the sides of a triangle, it shall cut the other sides, or those produced, proportionally : and if the sides, or the sides produced,...
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